https://github.com/rbind/simplystats
“R for Data Science”, Hadley Wickham & Garret Grolemund
https://www.gapminder.org/tools/#$state$time$value=2018;;&chart-type=bubbles
citation(package = "ggplot2")
##
## To cite ggplot2 in publications, please use:
##
## H. Wickham. ggplot2: Elegant Graphics for Data Analysis.
## Springer-Verlag New York, 2016.
##
## A BibTeX entry for LaTeX users is
##
## @Book{,
## author = {Hadley Wickham},
## title = {ggplot2: Elegant Graphics for Data Analysis},
## publisher = {Springer-Verlag New York},
## year = {2016},
## isbn = {978-3-319-24277-4},
## url = {http://ggplot2.org},
## }
citation(package = "tidyverse")
##
## To cite package 'tidyverse' in publications use:
##
## Hadley Wickham (2017). tidyverse: Easily Install and Load the
## 'Tidyverse'. R package version 1.2.1.
## https://CRAN.R-project.org/package=tidyverse
##
## A BibTeX entry for LaTeX users is
##
## @Manual{,
## title = {tidyverse: Easily Install and Load the 'Tidyverse'},
## author = {Hadley Wickham},
## year = {2017},
## note = {R package version 1.2.1},
## url = {https://CRAN.R-project.org/package=tidyverse},
## }
citation(package = "dslabs")
##
## To cite package 'dslabs' in publications use:
##
## Rafael A. Irizarry (2018). dslabs: Data Science Labs. R package
## version 0.5.2. https://CRAN.R-project.org/package=dslabs
##
## A BibTeX entry for LaTeX users is
##
## @Manual{,
## title = {dslabs: Data Science Labs},
## author = {Rafael A. Irizarry},
## year = {2018},
## note = {R package version 0.5.2},
## url = {https://CRAN.R-project.org/package=dslabs},
## }
##
## ATTENTION: This citation information has been auto-generated from
## the package DESCRIPTION file and may need manual editing, see
## 'help("citation")'.
install.packages("dslabs")
{dslabs} and other packages usedlibrary(tidyverse)
library(dslabs)
library(lubridate)
{ggplot2} is the core visualization packagedata("gapminder", package = "dslabs")
## ?gapminder for more info on the variables in the dataset
The gapminder dataset contains a number of measurements on health and income outcomes for 184 countries from 1960 to 2016. It also includes two character vectors, OECD and OPEC, with the names of OECD and OPEC countries from 2016.
gapminder dataset with Rgapminder <- gapminder %>% as_tibble()
gapminder %>% head(2)
## # A tibble: 2 x 9
## country year infant_mortality life_expectancy fertility population
## <fct> <int> <dbl> <dbl> <dbl> <dbl>
## 1 Albania 1960 115. 62.9 6.19 1636054
## 2 Algeria 1960 148. 47.5 7.65 11124892
## # … with 3 more variables: gdp <dbl>, continent <fct>, region <fct>
names(gapminder)
## [1] "country" "year" "infant_mortality"
## [4] "life_expectancy" "fertility" "population"
## [7] "gdp" "continent" "region"
gapminder %>%
ggplot(aes(x = fertility,
y = life_expectancy)) +
geom_point()
We call this ‘overplotting’.
This can be fixed in several ways:
- Reducing the transparency of data points
- Mapping colour to a variable (continuous or categorical)
- Reduce the data in the plot
- Mapping a shape to a variable
- Add noise (
"jitter") to points- Facetting - create panels for ‘categorical’ or so-called ‘factor’ variables in R
- Summarize the data
- Displaying a model / relationship that represents the data (and not sho the actual data itself)
- Or any combination of the above strategies
Basically you map an aesthetic (aes()) to a variable
Let’s go over these overplotting methods one by one
alpha) of points or lines in the datagapminder %>%
ggplot(aes(x = fertility,
y = life_expectancy)) +
geom_point(alpha = 0.1)
gapminder %>%
ggplot(aes(x = fertility,
y = life_expectancy)) +
geom_point(aes(colour = continent))
alphagapminder %>%
ggplot(aes(x = fertility,
y = life_expectancy)) +
geom_point(aes(colour = continent), alpha = 0.1) +
guides(colour = guide_legend(override.aes = list(alpha = 1)))
ggplot2 call. For example, adjust the alpha = ... or change the variable in x = ..., y = ... or colour = ...names(gapminder) gives you the variable names that you can changeguides(colour = guide_legend(override.aes = list(alpha = 1)))
#reduce_data_plot <- gapminder %>%
dplyr::filter(continent == "Africa" | continent == "Europe") %>%
ggplot(aes(x = fertility,
y = life_expectancy)) +
geom_point(aes(colour = continent), alpha = 0.2) +
## override the alpha setting for the points in the legend:
guides(colour = guide_legend(override.aes = list(alpha = 1)))
reduce_data_plot
aes() part of the geom_point() do?reduce_data_plot <- gapminder %>%
filter(continent == "Africa" | continent == "Europe") %>%
ggplot(aes(x = fertility,
y = life_expectancy, colour = continent)) +
geom_point(alpha = 0.2) +
## override the alpha setting for the points in the legend:
guides(colour = guide_legend(override.aes = list(alpha = 1)))
## or e.g. show only two years and map a shape to continent
shape_plot <- gapminder %>%
dplyr::filter(continent == "Africa" | continent == "Europe",
year == "1960" | year == "2010") %>%
ggplot(aes(x = fertility,
y = life_expectancy)) +
geom_point(aes(colour = as_factor(as.character(year)),
shape = continent),
alpha = 0.7)
as_factor(as.character(year)) call and replace this by only year above and rerun the plot, what happened?shape_plot
Create panels for ‘categorical’ or so-called ‘factor’ variables in R
facets_plot <- gapminder %>%
dplyr::filter(continent == "Africa" | continent == "Europe",
year == "1960" | year == "2010") %>%
ggplot(aes(x = fertility,
y = life_expectancy)) +
geom_point(aes(colour = continent), alpha = 0.5) +
facet_wrap(~ year)
facets_plot
library(ggrepel)
years <- c("1960", "1970", "1980", "1990", "2000", "2010")
summarize_plot <- gapminder %>%
dplyr::filter(year %in% years) %>%
group_by(continent, year) %>%
summarise(mean_life_expectancy = mean(life_expectancy),
mean_fertility = mean(fertility)) %>%
ggplot(aes(x = mean_fertility,
y = mean_life_expectancy)) +
geom_point(aes(colour = continent), alpha = 0.7)
summarize_plot
{ggrepel}library(ggrepel)
years <- c("1960", "1970", "1980", "1990", "2000", "2010")
labels_plot <- gapminder %>%
dplyr::filter(year %in% years) %>%
group_by(continent, year) %>%
summarise(mean_life_expectancy = mean(life_expectancy),
mean_fertility = mean(fertility)) %>%
ggplot(aes(x = mean_fertility,
y = mean_life_expectancy)) +
geom_point(aes(colour = continent), alpha = 0.7) +
geom_label_repel(aes(label=year), size = 2.5, box.padding = .5)
labels_plot
## Model
lm <- gapminder %>% lm(formula = life_expectancy ~ fertility)
correlation <- cor.test(x = gapminder$fertility,
y = gapminder$life_expectancy,
method = "pearson")
# save predictions of the model in the new data frame
# together with variable you want to plot against
predicted_df <- data.frame(gapminder_pred = predict(lm, gapminder),
fertility = gapminder$fertility)
model_plot <- gapminder %>%
ggplot(aes(x = fertility,
y = life_expectancy)) +
# geom_point(alpha = 0.03) +
geom_line(data = predicted_df, aes(x = fertility,
y = gapminder_pred),
colour = "darkred", size = 1)
model_plot
{ggpubr} packagegeom_smooth to display potential relationshipsgapminder %>%
ggplot(aes(x = fertility,
y = life_expectancy)) +
geom_point(alpha = 0.02) +
geom_smooth(method = "lm") +
stat_cor(method = "pearson", label.x = 2, label.y = 30) +
theme_bw()
Which tricks can we use to reduce the dimensionality of the plotted data (prevent overpltting)?
Try listing at least 6 methods:
gdp, Gross Domestic Product and infant_mortality rate.https://en.wikipedia.org/wiki/Gross_domestic_product Wikipedia: Gross Domestic Product (GDP) is a monetary measure of the market value of all the final goods and services produced in a period of time, often annually or quarterly. Nominal GDP estimates are commonly used to determine the economic performance of a whole country or region, and to make international comparisons.
gdp_infant_plot <- gapminder %>%
dplyr::filter(continent == "Europe" | continent == "Africa") %>%
ggplot(aes(x = gdp,
y = infant_mortality)) +
geom_point()
gdp_infant_plot
The figure above does not provide any clue on a possible difference between Europe and Africa, nor does it convey any information on trends over time.
colour_to_continent <- gapminder %>%
dplyr::filter(continent == "Europe" | continent == "Africa") %>%
ggplot(aes(x = gdp,
y = infant_mortality)) +
geom_point(aes(colour = continent))
colour_to_continent
Let’s investigate whether things have improved over time. We compare 1960 to 2010 by using a panel of two figures. Adding simply facet_wrap( ~ facetting_variable) will do the trick.
Without looking ahead try to contruct a plot that conveys information on the gdp per continent, over time. Try to recycle some of the examples above.
facets_gdp_infant <- gapminder %>%
dplyr::filter(continent == "Europe" | continent == "Africa",
year == "1960" | year == "2010") %>%
ggplot(aes(x = gdp,
y = infant_mortality)) +
geom_point(aes(colour = continent)) +
facet_wrap(~ year) +
theme(axis.text.x = element_text(angle = -90, hjust = 1))
facets_gdp_infant
So far we have been mapping colours and shapes to categorical variables. You can also map to continuous variables though.
continuous <- gapminder %>%
dplyr::filter(country == "Netherlands" |
country == "China" |
country == "India") %>%
dplyr::filter(year %in% years) %>%
ggplot(aes(x = year,
y = life_expectancy)) +
geom_point(aes(size = population, colour = country)) +
guides(colour = guide_legend(override.aes = list(alpha = 1))) +
geom_line(aes(group = country)) +
theme_bw()
continuous
Try plotting the infant_mortality against the filtered years for the same countries as the code above (Netherlands, India, China), recycling some of the code above. Discuss the resulting graph in the light of the life_expectancy graph, what do you think about the the developments in China?
Want to know more? see: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4331212/ Babxiarz, 2016
Analyze the following code chunk: try running line by line to see what happens:
group_by() statement, what happens if you do?population_plot <- gapminder %>%
dplyr::group_by(continent, year) %>%
dplyr::filter(year %in% years) %>%
summarise(sum_population = sum(population)) %>%
ggplot(aes(x = year,
y = sum_population)) +
geom_point(aes(colour = continent)) +
geom_line(aes(group = continent,
colour = continent))
population_plot
ranking_plot <- gapminder %>%
dplyr::filter(continent == "Europe",
year == 2010) %>%
ggplot(aes(x = reorder(as_factor(country), population),
y = log10(population))) +
geom_point() +
ylab("log10(Population)") +
xlab("Country") +
coord_flip() +
geom_point(data = filter(gapminder %>%
dplyr::filter(continent == "Europe",
year == 2010), population >= 1e7), colour = "red")
ranking_plot
We filter for “Americas” and “Oceania” and look at life_expectancy over the years.
## without summarizing for countries
gapminder$continent %>% as_factor() %>% levels()
## [1] "Africa" "Americas" "Asia" "Europe" "Oceania"
gapminder %>%
dplyr::filter(continent == "Americas" | continent == "Oceania") %>%
ggplot(aes(x = year,
y = life_expectancy)) +
geom_line(aes(group = continent,
colour = continent))
Obviously something went wrong here. Please, discuss with your neighbour what you think happened or needs to be done to fix this (without looking ahead ;-) )
We can see what happened if we plot individual datapoints
gapminder %>%
dplyr::filter(continent == "Americas" | continent == "Oceania") %>%
ggplot(aes(x = year,
y = life_expectancy)) +
geom_point(aes(colour = country)) +
theme(legend.position="none") +
facet_wrap( ~ continent) +
theme(legend.position="none")
gapminder$continent %>% as_factor() %>% levels()
## [1] "Africa" "Americas" "Asia" "Europe" "Oceania"
gapminder %>%
dplyr::filter(continent == "Americas" | continent == "Oceania") %>%
group_by(continent, year) %>%
summarise(mean_life_expectancy = mean(life_expectancy)) %>%
ggplot(aes(x = year,
y = mean_life_expectancy)) +
geom_line(aes(group = continent,
colour = continent)) +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
df <- gapminder %>%
dplyr::filter(continent == "Americas" | continent == "Oceania") %>%
group_by(continent, year)
model <- aov(data = df, life_expectancy ~ continent * year)
anova(model)
## Analysis of Variance Table
##
## Response: life_expectancy
## Df Sum Sq Mean Sq F value Pr(>F)
## continent 1 8982 8982 269.104 <2e-16 ***
## year 1 58606 58606 1755.931 <2e-16 ***
## continent:year 1 9 9 0.278 0.5981
## Residuals 2732 91183 33
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Some remarks on the above Two-way ANOVA:
Sometimes you have overlapping plots and adding transparency with alpha() or mapping colour to underlying categorical values is not working because there are simple to many points overlapping
Let’s look at an example
gapminder %>%
dplyr::filter(continent == "Americas" |
continent == "Africa") %>%
group_by(continent) %>%
dplyr::filter(year %in% years) %>%
ggplot(aes(x = year,
y = infant_mortality)) +
geom_point(aes(colour = country)) +
theme(legend.position="none")
In such cases it can be helpfull to add some noise to the points (position = "jitter") to reduce overlapping. This can be a powerfull approach, especially when combined with setting alpha()
gapminder %>%
dplyr::filter(continent == "Americas" |
continent == "Africa") %>%
dplyr::filter(year %in% years) %>%
group_by(continent) %>%
ggplot(aes(x = year,
y = infant_mortality)) +
geom_point(aes(colour = continent), position = "jitter")
It would be nice to know what the mean child mortality is for both continents
gapminder %>%
dplyr::filter(continent == "Americas" |
continent == "Africa") %>%
dplyr::filter(year %in% years) %>%
group_by(continent, year) %>%
summarise(mean_infant_mortality = mean(infant_mortality, na.rm = TRUE)) %>%
ggplot(aes(x = year,
y = mean_infant_mortality)) +
geom_col(aes(fill = continent), position = "dodge")
Now that we have the mean infant mortality for each year for the two continents, let’s add that data to the previous dot plot where we used jitter
mean_inf_mort <- gapminder %>%
dplyr::filter(continent == "Americas" |
continent == "Africa") %>%
dplyr::filter(year %in% years) %>%
group_by(continent, year) %>%
summarise(mean_infant_mortality = mean(infant_mortality, na.rm = TRUE))
gapminder %>%
dplyr::filter(continent == "Americas" |
continent == "Africa") %>%
dplyr::filter(year %in% years) %>%
group_by(continent) %>%
ggplot(aes(x = year,
y = infant_mortality)) +
geom_point(aes(colour = continent), position = "jitter") +
## summary data added to previous
geom_line(data = mean_inf_mort, aes(x = year,
y = mean_infant_mortality,
colour = continent), size = 2)
In the figure above we can observe a number of countries in ‘Americas’ continent that have a child mortality that are above the average (over the years) of ‘Africa’. Which countries are this?
library(ggiraph)
gapminder$country <-
str_replace_all(string = gapminder$country,
pattern = "'",
replacement = "_")
interactive_inf_mort <- gapminder %>%
dplyr::filter(continent == "Americas" |
continent == "Africa") %>%
dplyr::filter(year %in% years) %>%
group_by(region, country) %>%
ggplot(aes(x = year,
y = infant_mortality)) +
geom_point_interactive(aes(tooltip = country, colour = region), position = "jitter") +
# geom_point(aes(colour = continent), position = "jitter") +
## summary data added to previous
geom_line(data = mean_inf_mort, aes(x = year,
y = mean_infant_mortality,
colour = continent, group = continent), size = 2
)
interactive_inf_mort
gapminder$country %>% as_factor() %>% levels()
## [1] "Albania" "Algeria"
## [3] "Angola" "Antigua and Barbuda"
## [5] "Argentina" "Armenia"
## [7] "Aruba" "Australia"
## [9] "Austria" "Azerbaijan"
## [11] "Bahamas" "Bahrain"
## [13] "Bangladesh" "Barbados"
## [15] "Belarus" "Belgium"
## [17] "Belize" "Benin"
## [19] "Bhutan" "Bolivia"
## [21] "Bosnia and Herzegovina" "Botswana"
## [23] "Brazil" "Brunei"
## [25] "Bulgaria" "Burkina Faso"
## [27] "Burundi" "Cambodia"
## [29] "Cameroon" "Canada"
## [31] "Cape Verde" "Central African Republic"
## [33] "Chad" "Chile"
## [35] "China" "Colombia"
## [37] "Comoros" "Congo, Dem. Rep."
## [39] "Congo, Rep." "Costa Rica"
## [41] "Cote d_Ivoire" "Croatia"
## [43] "Cuba" "Cyprus"
## [45] "Czech Republic" "Denmark"
## [47] "Djibouti" "Dominican Republic"
## [49] "Ecuador" "Egypt"
## [51] "El Salvador" "Equatorial Guinea"
## [53] "Eritrea" "Estonia"
## [55] "Ethiopia" "Fiji"
## [57] "Finland" "France"
## [59] "French Polynesia" "Gabon"
## [61] "Gambia" "Georgia"
## [63] "Germany" "Ghana"
## [65] "Greece" "Greenland"
## [67] "Grenada" "Guatemala"
## [69] "Guinea" "Guinea-Bissau"
## [71] "Guyana" "Haiti"
## [73] "Honduras" "Hong Kong, China"
## [75] "Hungary" "Iceland"
## [77] "India" "Indonesia"
## [79] "Iran" "Iraq"
## [81] "Ireland" "Israel"
## [83] "Italy" "Jamaica"
## [85] "Japan" "Jordan"
## [87] "Kazakhstan" "Kenya"
## [89] "Kiribati" "South Korea"
## [91] "Kuwait" "Kyrgyz Republic"
## [93] "Lao" "Latvia"
## [95] "Lebanon" "Lesotho"
## [97] "Liberia" "Libya"
## [99] "Lithuania" "Luxembourg"
## [101] "Macao, China" "Macedonia, FYR"
## [103] "Madagascar" "Malawi"
## [105] "Malaysia" "Maldives"
## [107] "Mali" "Malta"
## [109] "Mauritania" "Mauritius"
## [111] "Mexico" "Micronesia, Fed. Sts."
## [113] "Moldova" "Mongolia"
## [115] "Montenegro" "Morocco"
## [117] "Mozambique" "Namibia"
## [119] "Nepal" "Netherlands"
## [121] "New Caledonia" "New Zealand"
## [123] "Nicaragua" "Niger"
## [125] "Nigeria" "Norway"
## [127] "Oman" "Pakistan"
## [129] "Panama" "Papua New Guinea"
## [131] "Paraguay" "Peru"
## [133] "Philippines" "Poland"
## [135] "Portugal" "Puerto Rico"
## [137] "Qatar" "Romania"
## [139] "Russia" "Rwanda"
## [141] "St. Lucia" "St. Vincent and the Grenadines"
## [143] "Samoa" "Saudi Arabia"
## [145] "Senegal" "Serbia"
## [147] "Seychelles" "Sierra Leone"
## [149] "Singapore" "Slovak Republic"
## [151] "Slovenia" "Solomon Islands"
## [153] "South Africa" "Spain"
## [155] "Sri Lanka" "Sudan"
## [157] "Suriname" "Swaziland"
## [159] "Sweden" "Switzerland"
## [161] "Syria" "Tajikistan"
## [163] "Tanzania" "Thailand"
## [165] "Timor-Leste" "Togo"
## [167] "Tonga" "Trinidad and Tobago"
## [169] "Tunisia" "Turkey"
## [171] "Turkmenistan" "Uganda"
## [173] "Ukraine" "United Arab Emirates"
## [175] "United Kingdom" "United States"
## [177] "Uruguay" "Uzbekistan"
## [179] "Vanuatu" "Venezuela"
## [181] "West Bank and Gaza" "Vietnam"
## [183] "Yemen" "Zambia"
## [185] "Zimbabwe"
ggiraph(ggobj = interactive_inf_mort)
west <- c("Western Europe","Northern Europe","Southern Europe",
"Northern America","Australia and New Zealand")
gapminder <- gapminder %>%
mutate(group = case_when(
region %in% west ~ "The West",
region %in% c("Eastern Asia", "South-Eastern Asia") ~ "East Asia",
region %in% c("Caribbean", "Central America", "South America") ~ "Latin America",
continent == "Africa" & region != "Northern Africa" ~ "Sub-Saharan Africa",
TRUE ~ "Others"))
gapminder <- gapminder %>%
mutate(group = factor(group, levels = rev(c("Others", "Latin America", "East Asia","Sub-Saharan Africa", "The West"))))
filter(gapminder, year%in%c(1962, 2013) & !is.na(group) &
!is.na(fertility) & !is.na(life_expectancy)) %>%
mutate(population_in_millions = population/10^6) %>%
ggplot( aes(fertility, y=life_expectancy, col = group, size = population_in_millions)) +
geom_point(alpha = 0.8) +
guides(size=FALSE) +
theme(plot.title = element_blank(), legend.title = element_blank()) +
coord_cartesian(ylim = c(30, 85)) +
xlab("Fertility rate (births per woman)") +
ylab("Life Expectancy") +
geom_text(aes(x=7, y=82, label=year), cex=12, color="grey") +
facet_grid(. ~ year) +
theme(strip.background = element_blank(),
strip.text.x = element_blank(),
strip.text.y = element_blank(),
legend.position = "top")
For this part we use a different and more simple dataset This dataset contains 1192 observations on self-reported:
height (inch)earn ($)sex (gender)ed (currently unannotated)age (years)raceheights_data <- read_csv(file = file.path(root,
"data",
"heights_outliers.csv"))
heights_data
## # A tibble: 1,192 x 6
## earn height sex ed age race
## <dbl> <dbl> <chr> <dbl> <dbl> <chr>
## 1 50000 74.4 male 16 45 white
## 2 60000 65.5 female 16 58 white
## 3 30000 63.6 female 16 29 white
## 4 50000 63.1 female 16 91 other
## 5 51000 63.4 female 17 39 white
## 6 9000 64.4 female 15 26 white
## 7 29000 61.7 female 12 49 white
## 8 32000 72.7 male 17 46 white
## 9 2000 72.0 male 15 21 hispanic
## 10 27000 72.2 male 12 26 white
## # … with 1,182 more rows
We will focus on the variable height here
summary_heights_data <- heights_data %>%
group_by(sex, age) %>%
summarise(mean_height = mean(height, na.rm = TRUE),
min_height = min(height),
max_height = max(height)) %>%
arrange(desc(mean_height))
summary_heights_data[c(1:4),]
## # A tibble: 4 x 5
## # Groups: sex [2]
## sex age mean_height min_height max_height
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 female 55 141. 61.9 664.
## 2 male 39 134. 66.6 572.
## 3 male 55 73.2 71.7 74.8
## 4 male 91 73.1 73.1 73.1
From the above summary we can conclude that there are two outliers (presumably entry errors).
Calculate the height in meters for each outlier in the Console 1 inch = 0,0254 meters
Please discuss the solution with your neighbour
heights_data %>%
ggplot(aes(x = height)) +
geom_histogram(aes(stat = "identity"), bins = 200)
This distribution looks odd. When you see a large x-axis with no data plotted on it, it usually means there is an outlier. If you look carefully, you will spot two outliers around 600
heights_data %>%
ggplot(aes(y = height)) +
geom_boxplot()
So apparantly there is one data point that is way off from the rest of the distribution. Let’s remove this point, using filter() from the {dplyr} package like we did before on the gapminder dataset.
heights_data %>%
dplyr::filter(height < 100) %>%
ggplot(aes(y = height)) +
geom_boxplot()
## by sex
heights_data %>%
dplyr::filter(height < 100) %>%
ggplot(aes(y = height, x = sex)) +
geom_boxplot()
Now let’s plot a new distribution plot, this time we plot density, leaving the outlier out
heights_data %>%
dplyr::filter(height < 100) %>%
ggplot(aes(height)) +
geom_freqpoly(aes(y = ..density..))
## by sex
heights_data %>%
dplyr::filter(height < 100) %>%
ggplot(aes(height)) +
geom_freqpoly(aes(y = ..density.., colour = sex))
## a qqplot provides a visual aid to assess whether a distribution is approaching normality
source(file = file.path(root, "code", "ggqq.R"))
height_data_outlier_removed <- heights_data %>%
dplyr::filter(height < 100)
gg_qq(height_data_outlier_removed$height)
## 25% 75%
## 66.926998 4.328462
## formal statistical proof
shapiro.test(height_data_outlier_removed$height)
##
## Shapiro-Wilk normality test
##
## data: height_data_outlier_removed$height
## W = 0.98485, p-value = 8.491e-10
all data -> reject hypothesis that the sample has a normal distribution
males <- height_data_outlier_removed %>%
dplyr::filter(sex == "male")
females <- height_data_outlier_removed %>%
dplyr::filter(sex == "female")
shapiro.test(males$height)
##
## Shapiro-Wilk normality test
##
## data: males$height
## W = 0.99053, p-value = 0.002532
shapiro.test(females$height)
##
## Shapiro-Wilk normality test
##
## data: females$height
## W = 0.99277, p-value = 0.002105
## add shapiro for each sex
## we can do the same for age
shapiro.test(males$age)
##
## Shapiro-Wilk normality test
##
## data: males$age
## W = 0.93358, p-value = 3.506e-14
shapiro.test(females$age)
##
## Shapiro-Wilk normality test
##
## data: females$age
## W = 0.93978, p-value = 4.862e-16